Regionalisation

In this note, we propose to test the use of the hierarchical classification algorithm with contiguity containment described in Guénard and Legendre (2022) and to apply it to FAO food balance sheets mesured in Kcal. The data are related to the year 2022, but it is possible to study time series back to 1961 under certain conditions (change in country borders, evolution of FAO nomenclature, etc.). It is alos possible to change the criteria of measurement, the graph of proximity, …

Data

Geometry

We select those countries in the world for which FAO data are available in 2022, removing Western Sahara and North Korea, for example. We keep small island states which will oblige us to choose a weight matrix different from classicall measure based on border contiguity.

Geopolitical network

As discussed in another part of the WorlRegio project (see. here)[https://worldregio.github.io/world_geom/geopolitical_network.html], thay are plenty of solutions for the elaboration of a network of proximity between states (i.e. a weight matrix that will be used as constraint in the clustering algorithm).

We choose here a method of Voronoï-Delaunay triangulation on map where we have used a polar projection on the North

As you can see, all states are connected, eventually at long distance as we can see in the example of the link between Canada and Korea or French Polynesia and Chile.

This solution is without any doubt likely to be criticized because it depends on the projection, on the choice of the center of states adopted, on the fact to keep or eliminate small states, etc. But our purpose is mainly pedagogical here and it is not the time to discuss the choice of the best geopolitical network. Just keep in mind that this choice has important implications on the results.

Dissimilarity matrix

We begin directly with the case of a dissimilarity matrix using all 95 items proposed by the FAO to describe a country’s diet. The table is of the following form. The unit of measurement is Kcal per person per day.

Données brutes

	2511	2513	2514	2515	2516	2517	2518	2520	2531	2532	2533	2534	2535	2536	2537	2541	2542	2543	2546	2547	2549	2551	2552	2555	2557	2558	2559	2560	2561	2563	2570	2571	2572	2573	2574	2575	2576	2577	2578	2579	2580	2581	2582	2586	2601	2602	2605	2611	2612	2613	2614	2615	2616	2617	2618	2619	2620	2625	2630	2633	2635	2640	2641	2642	2645	2655	2656	2657	2658	2680	2731	2732	2733	2734	2735	2736	2737	2740	2743	2744	2745	2761	2762	2763	2764	2765	2766	2767	2769	2775	2781	2782	2807	2848	2899
AFG	1317.18	0.52	45.63	1.39	0.06	0.60	0.06	5.74	44.33	0.02	0.00	0.00	0.00	0.00	0	0	83.18	1.51	0.00	16.99	9.83	21.05	4.28	0.05	0.00	0.60	0.0	0.04	10.88	0.01	0.25	2.58	0.00	24.55	0.29	3.81	0.07	152.66	0.00	1.46	0.56	0	0.16	30.26	0.00	6.60	33.40	2.07	0.01	0.00	1.07	4.25	0.00	9.28	0.01	4.31	23.87	11.49	0.02	0.86	0.16	0.09	0.00	0.03	3.35	0.00	0.00	0.00	0.00	0.25	11.22	18.90	0.03	3.29	1.05	3.21	8.26	21.14	0.03	2.47	0.30	0.69	0.00	0.12	0.01	0.00	0.00	0.00	0.00	0	0	0.00	202.34	85.27	3.42
AGO	138.23	0.00	409.17	0.00	0.44	6.57	0.00	0.19	13.90	748.76	100.23	0.01	0.00	0.00	0	0	81.73	8.57	53.75	0.00	6.86	1.06	38.49	6.04	0.00	0.08	0.0	0.26	1.30	0.15	0.00	72.25	21.37	5.68	0.08	0.25	5.53	124.92	0.08	0.00	2.53	0	0.01	17.06	9.26	0.14	26.96	0.18	0.02	0.00	19.95	68.73	0.00	0.27	14.73	0.03	0.05	28.25	0.80	1.91	0.02	0.03	0.02	0.00	0.18	2.66	40.25	27.01	4.71	1.34	18.96	2.81	54.30	39.62	1.07	7.77	7.39	0.78	0.54	6.28	5.63	2.45	3.34	17.96	1.58	0.08	0.01	0.00	0.00	0	0	0.00	129.37	17.64	4.19
ALB	854.36	1.92	21.71	5.00	1.53	0.00	0.00	0.71	88.70	0.01	0.05	0.00	0.00	0.00	0	0	189.24	39.97	44.64	0.02	4.41	54.97	6.05	0.03	0.00	0.66	0.0	0.91	0.00	37.13	0.00	6.15	1.25	91.46	0.06	0.00	0.00	0.00	0.00	0.00	119.67	0	6.00	27.94	53.67	37.60	160.22	15.64	3.25	0.04	0.19	16.83	0.00	47.30	0.17	21.17	131.89	83.24	2.16	29.69	0.22	0.23	2.06	0.00	0.16	5.41	44.41	0.02	9.80	1.61	76.02	46.59	35.57	85.67	1.98	18.07	51.30	22.76	1.69	59.16	16.25	3.30	1.49	7.40	0.63	1.53	1.90	0.25	0.00	0	0	0.00	57.52	609.73	20.12
ARE	860.55	0.03	24.84	0.03	1.02	0.00	0.00	0.49	59.22	2.54	2.02	0.45	0.68	0.08	0	0	207.81	18.13	28.29	28.12	113.04	39.88	9.26	0.86	2.56	0.94	9.8	9.13	12.62	5.93	0.21	50.78	3.59	21.71	124.82	0.58	1.87	317.36	13.85	1.45	34.97	0	31.31	18.98	4.78	21.64	56.75	12.22	3.91	0.39	0.76	21.22	3.94	19.39	1.93	44.38	6.33	21.03	0.61	24.14	0.08	2.68	8.64	0.00	12.83	4.10	6.80	0.11	0.00	3.74	58.67	44.37	4.25	208.40	12.10	7.93	17.11	48.79	0.00	41.10	8.59	11.54	8.44	23.39	0.81	1.17	1.64	0.31	0.00	0	0	0.00	310.26	156.85	13.49
ARG	876.56	0.00	93.00	0.00	7.55	0.00	0.00	3.33	64.34	5.65	6.49	0.00	0.00	0.00	0	0	309.25	61.68	36.14	27.18	18.95	5.53	25.99	0.02	0.00	0.00	0.0	1.18	0.00	1.99	0.00	66.60	21.04	287.14	1.32	1.19	0.00	0.00	1.09	0.02	5.52	0	30.02	14.43	15.72	11.83	28.87	23.83	7.73	0.82	0.04	23.86	0.11	5.89	0.65	0.06	5.95	16.92	2.06	12.41	8.22	0.33	0.90	0.01	1.10	40.88	50.83	0.23	12.21	0.00	257.46	5.67	107.37	181.84	4.39	34.52	104.41	11.27	0.57	55.44	0.29	0.82	3.52	3.85	0.00	2.12	0.58	0.64	0.00	0	0	0.01	69.92	258.03	0.00
ARM	928.54	56.05	43.46	3.85	11.07	0.00	0.00	32.76	122.83	0.00	0.01	0.00	0.00	0.00	0	0	259.17	40.41	7.47	14.32	10.29	26.30	10.69	0.16	0.00	0.17	0.0	0.78	1.42	4.66	0.85	3.62	0.03	199.53	0.02	0.00	0.00	0.00	2.45	0.20	1.55	0	3.26	47.26	27.71	10.75	110.98	11.19	1.38	0.60	0.05	15.30	0.00	19.35	0.76	2.31	18.17	93.77	6.24	59.00	0.05	0.71	1.17	0.00	0.36	3.79	14.11	0.00	5.57	1.82	138.20	23.54	68.92	70.07	0.20	21.92	135.47	11.82	22.88	50.18	6.86	7.35	0.09	2.53	0.41	0.52	0.02	0.03	0.00	0	0	0.00	39.93	414.62	22.91
ATG	494.44	0.09	13.87	0.01	12.60	0.00	0.00	2.42	40.46	4.47	4.55	3.18	4.35	0.00	0	0	180.99	30.88	9.08	3.47	10.78	2.72	11.11	0.71	0.85	3.84	0.0	7.13	1.03	0.94	0.65	90.49	1.85	0.97	10.80	0.04	0.00	0.00	1.59	1.47	22.02	0	2.86	106.71	4.08	5.98	44.94	24.35	4.54	2.12	3.23	21.00	8.59	8.44	3.52	0.87	5.96	130.80	7.94	24.48	0.09	3.65	1.68	0.60	12.50	24.09	30.86	7.51	60.73	7.88	47.24	6.67	63.59	258.92	1.18	9.52	86.81	34.79	18.93	35.42	2.95	2.32	5.35	27.14	50.75	6.33	0.84	3.35	0.00	0	0	1.44	94.06	148.51	18.48
AUS	542.77	0.00	28.54	0.19	0.51	0.00	0.06	12.89	86.74	0.82	6.61	0.30	0.03	0.00	0	0	345.02	73.11	32.89	8.19	27.47	84.12	28.37	1.55	0.00	0.49	0.0	8.29	0.00	2.80	0.01	11.07	1.31	14.10	279.43	47.51	0.00	49.83	1.97	4.68	48.22	0	1.74	143.35	12.25	10.31	54.25	7.83	0.76	0.15	0.95	17.44	0.00	16.71	4.33	1.31	9.12	45.57	7.11	25.13	0.22	1.10	1.83	0.05	3.64	65.59	106.05	2.17	51.66	0.00	96.62	58.57	108.68	185.62	3.00	27.04	50.41	74.21	1.83	24.83	4.53	8.59	5.30	12.82	5.23	4.17	2.48	1.09	0.08	0	0	0.10	83.69	330.74	40.55
AUT	677.19	2.44	83.33	66.75	20.51	0.00	0.00	15.01	82.13	0.00	1.19	0.06	0.00	0.00	0	0	330.64	42.62	1.49	1.93	12.48	37.55	19.76	40.37	12.74	0.31	0.0	2.92	2.06	2.35	2.52	62.14	1.62	130.26	208.37	0.00	0.00	0.00	12.92	0.36	25.74	0	0.00	218.46	14.99	10.20	56.01	13.93	2.78	0.36	1.04	30.74	0.02	35.77	4.42	1.35	8.04	44.05	3.31	13.71	0.15	1.91	2.85	0.05	5.86	59.42	127.72	0.23	21.34	0.06	55.04	5.89	199.15	71.88	1.57	13.49	228.94	114.25	48.67	52.92	8.83	7.46	4.44	11.35	1.41	1.53	0.53	0.23	0.02	0	0	0.01	36.68	369.33	0.00
AZE	1247.15	39.55	76.99	1.67	1.63	0.00	0.00	11.50	158.27	0.00	0.00	0.00	0.00	0.00	0	0	250.58	37.72	6.20	6.83	6.83	51.13	10.29	0.02	0.00	0.09	0.0	0.85	0.00	0.57	0.00	4.37	0.00	77.84	2.78	0.00	0.00	0.05	1.45	0.01	3.11	0	29.45	154.75	36.55	25.12	66.36	7.14	1.92	0.08	0.62	9.07	0.00	21.60	0.25	3.90	31.79	54.65	1.93	31.81	0.50	0.30	0.16	0.00	1.13	1.76	5.95	0.06	86.01	1.93	83.56	52.23	5.38	60.67	0.01	15.90	65.91	82.57	0.04	34.42	5.45	1.36	0.18	2.45	0.32	0.04	0.02	0.01	0.00	0	0	0.00	52.29	283.07	9.38

Profil en ligne

	2511	2513	2514	2515	2516	2517	2518	2520	2531	2532	2533	2534	2535	2536	2537	2541	2542	2543	2546	2547	2549	2551	2552	2555	2557	2558	2559	2560	2561	2563	2570	2571	2572	2573	2574	2575	2576	2577	2578	2579	2580	2581	2582	2586	2601	2602	2605	2611	2612	2613	2614	2615	2616	2617	2618	2619	2620	2625	2630	2633	2635	2640	2641	2642	2645	2655	2656	2657	2658	2680	2731	2732	2733	2734	2735	2736	2737	2740	2743	2744	2745	2761	2762	2763	2764	2765	2766	2767	2769	2775	2781	2782	2807	2848	2899
AFG	58.71	0.02	2.03	0.06	0.00	0.03	0	0.26	1.98	0.00	0.00	0.00	0.00	0	0	0	3.71	0.07	0.00	0.76	0.44	0.94	0.19	0.00	0.00	0.03	0.0	0.00	0.48	0.00	0.01	0.12	0.00	1.09	0.01	0.17	0.00	6.80	0.00	0.07	0.02	0	0.01	1.35	0.00	0.29	1.49	0.09	0.00	0.00	0.05	0.19	0.00	0.41	0.00	0.19	1.06	0.51	0.00	0.04	0.01	0.00	0.00	0	0.15	0.00	0.00	0.00	0.00	0.01	0.50	0.84	0.00	0.15	0.05	0.14	0.37	0.94	0.00	0.11	0.01	0.03	0.00	0.01	0.00	0.00	0.00	0.00	0	0	0	0	9.02	3.80	0.15
AGO	5.68	0.00	16.80	0.00	0.02	0.27	0	0.01	0.57	30.75	4.12	0.00	0.00	0	0	0	3.36	0.35	2.21	0.00	0.28	0.04	1.58	0.25	0.00	0.00	0.0	0.01	0.05	0.01	0.00	2.97	0.88	0.23	0.00	0.01	0.23	5.13	0.00	0.00	0.10	0	0.00	0.70	0.38	0.01	1.11	0.01	0.00	0.00	0.82	2.82	0.00	0.01	0.60	0.00	0.00	1.16	0.03	0.08	0.00	0.00	0.00	0	0.01	0.11	1.65	1.11	0.19	0.06	0.78	0.12	2.23	1.63	0.04	0.32	0.30	0.03	0.02	0.26	0.23	0.10	0.14	0.74	0.06	0.00	0.00	0.00	0	0	0	0	5.31	0.72	0.17
ALB	25.20	0.06	0.64	0.15	0.05	0.00	0	0.02	2.62	0.00	0.00	0.00	0.00	0	0	0	5.58	1.18	1.32	0.00	0.13	1.62	0.18	0.00	0.00	0.02	0.0	0.03	0.00	1.10	0.00	0.18	0.04	2.70	0.00	0.00	0.00	0.00	0.00	0.00	3.53	0	0.18	0.82	1.58	1.11	4.73	0.46	0.10	0.00	0.01	0.50	0.00	1.40	0.01	0.62	3.89	2.46	0.06	0.88	0.01	0.01	0.06	0	0.00	0.16	1.31	0.00	0.29	0.05	2.24	1.37	1.05	2.53	0.06	0.53	1.51	0.67	0.05	1.74	0.48	0.10	0.04	0.22	0.02	0.05	0.06	0.01	0	0	0	0	1.70	17.98	0.59
ARE	25.91	0.00	0.75	0.00	0.03	0.00	0	0.01	1.78	0.08	0.06	0.01	0.02	0	0	0	6.26	0.55	0.85	0.85	3.40	1.20	0.28	0.03	0.08	0.03	0.3	0.27	0.38	0.18	0.01	1.53	0.11	0.65	3.76	0.02	0.06	9.55	0.42	0.04	1.05	0	0.94	0.57	0.14	0.65	1.71	0.37	0.12	0.01	0.02	0.64	0.12	0.58	0.06	1.34	0.19	0.63	0.02	0.73	0.00	0.08	0.26	0	0.39	0.12	0.20	0.00	0.00	0.11	1.77	1.34	0.13	6.27	0.36	0.24	0.52	1.47	0.00	1.24	0.26	0.35	0.25	0.70	0.02	0.04	0.05	0.01	0	0	0	0	9.34	4.72	0.41
ARG	26.19	0.00	2.78	0.00	0.23	0.00	0	0.10	1.92	0.17	0.19	0.00	0.00	0	0	0	9.24	1.84	1.08	0.81	0.57	0.17	0.78	0.00	0.00	0.00	0.0	0.04	0.00	0.06	0.00	1.99	0.63	8.58	0.04	0.04	0.00	0.00	0.03	0.00	0.16	0	0.90	0.43	0.47	0.35	0.86	0.71	0.23	0.02	0.00	0.71	0.00	0.18	0.02	0.00	0.18	0.51	0.06	0.37	0.25	0.01	0.03	0	0.03	1.22	1.52	0.01	0.36	0.00	7.69	0.17	3.21	5.43	0.13	1.03	3.12	0.34	0.02	1.66	0.01	0.02	0.11	0.12	0.00	0.06	0.02	0.02	0	0	0	0	2.09	7.71	0.00

The code of products will probably look very abstract for the reader but you can find more detailed explication on FAO website

To measure the dissimilarity between two countries, we decide to use the Whittaker distance measure, which is the sum of the absolute values of the percentage differences divided by 2 :

\(D_{ij} = \frac{1}{2}\sum_{k=1}^K |\frac{x_{ik}}{x_{i.}}-\frac{x_{jk}}{x_{j.}}|\)

Calculation is very easy with the dist.ldc function of the package adespatial, which is optimized for calculation on large arrays (which is not the case here).

Info -- For this coefficient, sqrt(D) would be Euclidean

Extrait de la matrice de dissimilarité

	AFG	AGO	ALB	ARE	ARG
AFG	0.000	0.719	0.521	0.370	0.526
AGO	0.719	0.000	0.737	0.658	0.680
ALB	0.521	0.737	0.000	0.382	0.345
ARE	0.370	0.658	0.382	0.000	0.367
ARG	0.526	0.680	0.345	0.367	0.000

As in the case of the geopolitical network, the choice of the dissimilarity matrix is likely to be criticized because they are many possible options that could obviously produce different results. We could firstly choose another measuer of dissimilarity (many of them are presented and discussed in Guénard and Legendre (2022)). But we could also decide to use a different weight for the measure of the role of the 95 food items. Instead of Kcal/, we could have simply use the Kg/capita. Another option could be to focus on proteins or fat present in each item. In this cases some items would have an increase or decrease of their influence in the elaboration of dissimilarity. Last but not least, the level of disaggregation of food items would modify the results (consider the case of oils …).

Classification

Having defined the weight matrix and the dissimilarity matrix, we can move on to classification, which is carried out using the constr.hclust() function from the adespatial package, whose instructions for use are nicely described in Guénard and Legendre (2022) with an example.

Tree

As in a classical hierarchical classification, we have to analyse the tree before to take a decision on the number of regions we want to build.

The choice is not obvious but we can start with a division in 6 classes

Network visualization of regions

The adespatial package allows us to visualize the result in the form of a graph. The borders of the corresponding countries are superimposed on the graph.

One of the most interesting results of this example if the fact that the regions obtained does not necessarily follow the usual limits of continents, precisely because we have selected a Voronoï-Delaunay network that made possible links at long distance. Two examples can illustrate this point :

• The region represented in gray associates Europe (including Russia), USA, Canada, Chile, Argentina, Uruguay, Australia and New-Zealand, creating a very good approximation of the so-called “Global North” or “Western”. This result was possible only because of the long distance links creating by the Voronoï-Delaunay network across the Pacific through the … territory of French Polynesia. Should we have eliminated this entity, such a region would not have come to existence !

• The region represented in blue is associated to the majority of muslim countries and associate Northern Africa with Middle East, Central Asia and part of the Indian Ocean. Huntington’s fan would probably interpret this result through the lenz of religion (e.g. the fact that alcohol is forbidden) but it is not perfectly true because many other products contribute to the result as we will see below. And as in the previous case, the result is strongly dependent from the geopolitical network adopted.

To summarize : this example illustrate that regionalizations of the world based on a criterium of homogeneity are always a compromise between the choice of the geopolitical network used as weight matrix and the choice of the dissimilarity measure. The big danger from scientific point of view is to consider that only one factor is at stake when both are clearly combined.

Specificities of region

We use the catdes() function from the FactoMineR package to analyze class profiles.

Specificities of the regions in terms of energy supply measured in Kcal)

	Under-représentation (z-score < -3)	Over-représentation (z-score > +3)
Reg. 1	Beer, Pigmeat	Wheat and products, Dates, Mutton & Goat Meat, Tomatoes and products, Onions, Nuts and products, Maize Germ Oil, Olives (including preserved)
Reg. 2	Soyabean Oil; Lemons, Limes and products; Grapes and products (excl wine); Oats; Beer; Fruits, other; Sunflowerseed Oil; Cocoa Beans and products; Vegetables, other; Oilcrops Oil, Other; Beverages, Alcoholic; Sweeteners, Other; Nuts and products; Fats, Animals, Raw; Butter, Ghee; Pigmeat; Oranges, Mandarines; Apples and products; Potatoes and products; Poultry Meat; Milk - Excluding Butter; Eggs; Sugar (Raw Equivalent); Wheat and products	Groundnuts; Cassava and products; Sorghum and products; Groundnut Oil; Oilcrops, Other; Yams; Millet and products; Sesame seed; Beverages, Fermented; Plantains; Palm Oil; Palmkernel Oil; Pulses, Other and products
Reg. 3	Pulses, Other and products, Cassava and products, Maize and products, Palm Oil, Rice and products	Milk - Excluding Butter, Wine, Beer, Pigmeat, Butter, Ghee, Potatoes and products, Honey, Fats, Animals, Raw, Sunflowerseed Oil, Apples and products, Cream, Cocoa Beans and products, Rye and products, Oilcrops Oil, Other, Oats, Eggs, Nuts and products, Wheat and products, Sweeteners, Other, Rape and Mustard Oil, Grapes and products (excl wine), Olive Oil, Bovine Meat, Demersal Fish, Beverages, Alcoholic, Sugar (Raw Equivalent), Coffee and products, Tomatoes and products, Oranges, Mandarines
Reg. 4	Sunflowerseed Oil; Nuts and products	Pineapples and products; Poultry Meat; Soyabean Oil; Oranges, Mandarines; Lemons, Limes and products; Infant food; Sugar (Raw Equivalent); Grapefruit and products; Fruits, other; Maize and products
Reg. 5	Tomatoes and products; Wheat and products	Rice and products; Freshwater Fish; Ricebran Oil; Sugar cane; Pimento; Palmkernel Oil
Reg. 6	Vegetables, other, Poultry Meat, Eggs	Maize and products, Beverages, Fermented
Reg. 7	Milk - Excluding Butter	Coconuts - Incl Copra; Coconut Oil; Aquatic Animals, Others; Molluscs, Other; Marine Fish, Other; Roots, Other; Aquatic Plants; Pelagic Fish; Pigmeat; Sweet potatoes; Soyabeans; Miscellaneous; Poultry Meat; Vegetables, other; Cephalopods; Crustaceans

Final map

References

Guénard, Guillaume, and Pierre Legendre. 2022. “Hierarchical Clustering with Contiguity Constraint in r.” Journal of Statistical Software 103: 126. https://www.jstatsoft.org/article/view/v103i07.